If R[x] is a P.I.D. and R commutative, then R is a field Post published:June 27, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingIf R[x] is a P.I.D. and R commutative, then R is a field
A subring R of the PID R[x] is an integral domain Post published:June 23, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingA subring R of the PID R[x] is an integral domain
Any two nonzero elements of a principal ideal domain have a least common multiple Post published:June 21, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingAny two nonzero elements of a principal ideal domain have a least common multiple
Two ideals (a) and (b) in PID are comaximal iff gcd(a,b) = 1 Post published:June 19, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingTwo ideals (a) and (b) in PID are comaximal iff gcd(a,b) = 1
A quotient of a principal ideal domain by a prime is again a P.I.D. Post published:June 15, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingA quotient of a principal ideal domain by a prime is again a P.I.D.
Every nonzero prime ideal in a P.I.D. is a maximal ideal Post published:June 13, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingEvery nonzero prime ideal in a P.I.D. is a maximal ideal
An element of minimum norm in Euclidean Domain is a unit Post published:June 7, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingAn element of minimum norm in Euclidean Domain is a unit
If R is a Euclidean domain, then there are universal side divisors in R Post published:June 2, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingIf R is a Euclidean domain, then there are universal side divisors in R
The integers are a Euclidean Domain Post published:May 28, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingThe integers are a Euclidean Domain
Fields are Euclidean Domains Post published:May 24, 2023 Post category:Mathematics/Ring Theory Post comments:0 Comments Continue ReadingFields are Euclidean Domains